Answer :
To solve this problem we will apply the concepts related to the change of the momentum. At the same time we will use Newton's second law to obtain the acceleration of the object and the kinematic equations of linear motion.
Newton's second law is defined as,
[tex]F = ma \rightarrow a = \frac{F}{m}[/tex]
Here,
F = Force
m = Mass
a = Acceleration
Our values are given as,
[tex]v_i = 0.8 m/s[/tex]
[tex]v_f = ?[/tex]
[tex]t = 1.5s[/tex]
[tex]F = -0.3N[/tex]
According to this values we have that the acceleration is,
[tex]a = \frac{F}{m}[/tex]
[tex]a = \frac{-0.3}{0.8}[/tex]
[tex]a = -0.375m/s^2[/tex]
Now applying the concepts of kinematic equations we have that the final velocity is,
[tex]v_f = v_i + at[/tex]
[tex]v_f = 0.8m/s + (-0.375m/s^2)(1.5s)[/tex]
[tex]v_f = 0.3375m/s[/tex]
By definition we know that momentum is the product between mass and velocity, so the change in momentum would be given by
[tex]\Delta p = p_f - p_i[/tex]
[tex]\Delta p = mv_f-mv_i[/tex]
[tex]\Delta p = m(v_f-v_i)[/tex]
[tex]\Delta p = (0.8)(0.3375-0.9)[/tex]
[tex]\Delta p = - 0.45kg \cdot m/s[/tex]
Therefore the change in momentum of the fancart is -0.45kg m/s
The change in the momentum of the fan cart is -0.45 kgm/s.
Mass of the fan cart m = 0.8kg.
The initial velocity of the fan cart u = < 0.8, 0, 0 > m/s
Constant force acting on the cart F = < −0.3, 0, 0 > N
Acceleration:
From Newton's Laws of motion:
F = ma,
where a is the acceleration
a = F/m
a = < −0.3, 0, 0 > / 0.8
a = < −0.375, 0, 0 > m/s²
Momentum:
the magnitude of initial velocity is u = 8m/s and the magnitude of the acceleration is a = −0.375m/s²
From the first equation of motion, the final velocity of the fan cart is:
v = u + at
v = 8 - 0.375×1.5 m/s
v = 7.43 m/s
The change in linear momentum is given by:
Δp = mv - mu
Δp = m(v-u)
Δp = 0.8(-0.57) kgm/s
Δp = -0.45 kgm/s
Learn more about linear momentum:
https://brainly.com/question/24592032?referrer=searchResults